Let a =2 i -5 j +5 k and b = i - j +3 k. If c is a vector such that 2( a × c )+3( b × c )= 0 and ( a - b ) · c =-97, then | c × k |^2 is equal to

Let $\displaystyle \vec{a}=2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\displaystyle \vec{b}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\displaystyle \vec{c}$ is a vector such that $\displaystyle 2(\vec{a} \times \vec{c})+3(\vec{b} \times \vec{c})=\overrightarrow{0}$ and $\displaystyle (\vec{a}-\vec{b}) \cdot \vec{c}=-97$, then $\displaystyle |\vec{c} \times \hat{\mathrm{k}}|^2$ is equal to